Method and apparatus for determining a quality metric of a measurement of a fluid parameter

ABSTRACT

An apparatus for measuring a parameter of a fluid passing through a pipe includes a spatial array of at least two sensors disposed at different axial locations along the pipe. Each of the sensors provides a signal indicative of unsteady pressure within the pipe at a corresponding axial location of the pipe. A signal processor constructs at least a portion of a k-ω plot using the signals and detects at least one ridge in the k-ω plot. A slope of the at least one ridge is indicative of the parameter of the fluid. The signal processor determines a quality metric by comparing an accumulated energy (power) of k-ω pairs along the at least one ridge with an accumulated energy (power) of k-ω pairs along at least one ray extending in the k-ω plot. The quality metric is indicative of a quality of the at least one ridge.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

The present application claims the benefit of U.S. Provisional PatentApplication No. 60/528,731, (CiDRA Docket No. CC-0684) filed Dec. 11,2003, which is incorporated by reference herein in its entirety.

TECHNICAL FIELD

This invention relates to a method and apparatus for measuring at leastone parameter of a fluid flowing within a pipe. More specifically, thisinvention relates to a method and apparatus for determining a qualitymetric of the measurement of the fluid parameter.

BACKGROUND

A fluid flow process (flow process) includes any process that involvesthe flow of fluid through pipes, ducts, or other conduits, as well asthrough fluid control devices such as pumps, valves, orifices, heatexchangers, and the like. Flow processes are found in many differentindustries such as the oil and gas industry, refining, food and beverageindustry, chemical and petrochemical industry, pulp and paper industry,power generation, pharmaceutical industry, and water and wastewatertreatment industry. The fluid within the flow process may be a singlephase fluid (e.g., gas, liquid or liquid/liquid mixture) and/or amulti-phase mixture (e.g. paper and pulp slurries or other-solid/liquidmixtures). The multi-phase mixture may be a two-phase liquid/gasmixture, a solid/gas mixture or a solid/liquid mixture, gas entrainedliquid or a three-phase mixture.

Various sensing technologies exist for measuring various physicalparameters of fluids in an industrial flow process. Such physicalparameters may include, for example, volumetric flow rate, composition,gas volume fraction, consistency, density, and mass flow rate.

One such sensing technology is described in commonly-owned U.S. Pat. No.6,609,069 to Gysling, entitled “Method and Apparatus for Determining theFlow Velocity Within a Pipe”, which is incorporated herein by reference.The '069 patent describes a method and corresponding apparatus formeasuring the flow velocity of a fluid in an elongated body (pipe) bysensing vortical disturbances convecting with the fluid. The methodincludes the steps of: providing an array of at least two sensorsdisposed at predetermined locations along the elongated body, eachsensor for sampling the pressure of the fluid at the position of thesensor at a predetermined sampling rate; accumulating the sampled datafrom each sensor at each of a number of instants of time spanning apredetermined sampling duration; and constructing from the accumulatedsampled data at least a portion of a so called k-ω plot, where the k-ωplot is indicative of a dispersion relation for the propagation ofacoustic pressures emanating from the vortical disturbances. The methodalso includes the steps of: identifying a convective ridge in the k-ωplot; determining the orientation of the convective ridge in the k-ωplot; and determining the flow velocity based on a predeterminedcorrelation of the flow velocity with the slope of the convective ridgeof the k-ω plot.

Another such sensing technology is described in commonly-owned U.S. Pat.Nos. 6,354,147 and 6,732,575 to Gysling et. al, both of which areincorporated by reference herein in their entirety. The '147 and '575patents describe a spatial array of acoustic pressure sensors placed atpredetermined axial locations along a pipe. The pressure sensors provideacoustic pressure signals to signal processing logic which determinesthe speed of sound of the fluid (or mixture) in the pipe using any of anumber of acoustic spatial array signal processing techniques with thedirection of propagation of the acoustic signals along the longitudinalaxis of the pipe. The speed of sound is provided to logic, whichcalculates the percent composition of the mixture, e.g., water fraction,or any other parameter of the mixture, or fluid, that is related to thesound speed. The logic may also determine the Mach number of the fluid.

Such sensing technologies are effective in determining variousparameters of a fluid flow within a pipe. However, as with anycomputationally complex process, there remains a desire to increasecomputational efficiency and accuracy.

SUMMARY OF THE INVENTION

The above-described and other needs are met by an apparatus, method, andstorage medium of the present invention, wherein a parameter of a fluidpassing through a pipe is measured using a spatial array of at least twosensors disposed at different axial locations along the pipe. Each ofthe sensors provides a signal indicative of unsteady pressure within thepipe at a corresponding axial location of the pipe. At least a portionof a k-ω plot is constructed from the signals, where the k-ω plot isindicative of a dispersion relation for the unsteady pressure within thepipe. At least one ridge in the k-ω plot is detected and an accumulatedenergy for k-ω pairs along the at least one ridge is determined. A slopeof the at least one ridge is indicative of the parameter of the fluid.The accumulated energy for k-ω pairs along the at least one ridge iscompared to an accumulated energy for k-ω pairs along at least one rayextending in the k-ω plot to determine a quality metric indicative of aquality of the at least one ridge. The quality metric may be compared toa threshold value, and, in response to the quality metric exceeding thethreshold value, a parameter of the fluid is determined using the slopeof the at least one ridge. The parameter of the fluid may include atleast one of: velocity of the fluid and speed of sound of the fluid.

The accumulated energy for k-ω pairs along the at least one ridge may bedetermined as a sum of the powers associated with the k-ω pairs alongthe at least one ridge. Similarly, the accumulated energy for k-ω pairsalong the at least one ray may be determined as a sum of the powersassociated with the k-ω pairs along the at least one ray. Alternatively,the accumulated energy for k-ω pairs along the at least one ray may bedetermined as an average accumulated energy for k-ω pairs along aplurality of rays.

In various embodiments, the at least one ridge includes a first acousticridge in a left plane of the k-ω plot and a second acoustic ridge in theright plane of the k-ω plot. The accumulated energy for k-ω pairs alongthe at least one ridge is a sum of the powers associated with the k-ωpairs along the first and second acoustic ridges.

In various embodiments, the at least one ray has a slope indicative of areference velocity, and the slope of the at least one ridge isindicative of a best velocity. The reference velocity may be determinedas a function of the best velocity (e.g., a percentage of the bestvelocity) or may be independent of the best velocity (e.g., a maximum orminimum velocity). The quality metric may be determined using theequation:$Q = \frac{P_{{BEST}\quad{VELOCITY}} - P_{REFERNCE}}{P_{{BEST}\quad{VELOCITY}} + P_{REFERNCE}}$where P_(best velocity) is the accumulated energy for k-ω pairs alongthe at least one ridge in a linear scale, P_(reference) is theaccumulated energy for k-ω pairs along the at least one ray in a linearscale, and Q is the quality metric.

In one aspect, accumulated energies for a plurality of rays in the k-ωplot are determined, wherein the slopes of the plurality of raysindicate a plurality of trial velocities. The reference velocity is thenselected from the trial velocities by comparing the accumulated energiesfor the plurality of rays. The trial velocities may include: a trialvelocity determined as a function of the best velocity (e.g., apercentage of the best velocity) and a trial velocity independent of thebest velocity (e.g., a maximum or minimum trial velocity).

In any of the embodiments described herein, the at least two pressuresensors may be selected from a group consisting of: piezoelectric,piezoresistive, strain gauge, PVDF, optical sensors, ported ac pressuresensors, accelerometers, velocity sensors, and displacement sensors. Invarious embodiments, the at least two pressure sensors are wrappedaround at least a portion of the pipe and do not contact the fluid.

The foregoing and other objects, and features of the present inventionwill become more apparent in light of the following detailed descriptionof exemplary embodiments thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring now to the drawing wherein like items are numbered alike inthe various Figures:

FIG. 1 is schematic diagram of an apparatus for determining at least oneparameter associated with a fluid flowing in a pipe in accordance withvarious embodiments of the present invention.

FIG. 2 is a flow chart depicting a method used in the apparatus of thepresent invention for determining the quality of a ridge identified inthe k-ω plane.

FIG. 3 is a block diagram of a first embodiment of a flow logic used inthe apparatus of the present invention.

FIG. 4 is a cross-sectional view of a pipe having coherent structurestherein.

FIG. 5 a k-ω plot of data processed from an apparatus embodying thepresent invention that illustrates slope of the convective ridge, and aplot of the optimization function of the convective ridge.

FIG. 6 is a plot of accumulated energy (dB) for trial velocities rangingfrom about 4.5 ft/sec to about 30 ft/sec.

FIG. 7 is a block diagram of a second embodiment of a flow logic used inthe apparatus of the present invention.

FIG. 8 a k-ω plot of data processed from an apparatus embodying thepresent invention that illustrates slope of the acoustic ridges.

FIG. 9 is a plot of accumulated energy (dB) for trial velocities rangingfrom about 713 ft/sec to about 5000 ft/sec.

FIG. 10 is a plot of mixture sound speed as a function of gas volumefraction for a 5% consistency slurry over a range of process pressures.

FIG. 11 is a plot of sound speed as a function of frequency forair/particle mixtures with fixed particle size and varyingair-to-particle mass ratio.

FIG. 12 is a plot of sound speed as a function of frequency forair/particle mixtures with fixed air-to-particle mass ration and fixedparticle size.

DETAILED DESCRIPTION

As described in U.S. Pat. No. 6,354,147, filed on Jun. 25, 1999, U.S.Pat. No. 6,691,584, filed on Jul. 2, 1999, U.S. Pat. No. 6,587,798,filed on Nov. 28, 2001, U.S. Pat. No. 6,609,069, filed on Dec. 4, 2000,U.S. patent application Ser. No. 10/349,716 (Atty. Docket no. CC-0579),filed on Jan. 23, 2003, and U.S. patent application Ser. No. 10/376,427(Atty. Docket no. CC-0596), filed on Feb. 26, 2003, which are allincorporated herein by reference, unsteady pressures along a pipe, asmay be caused by one or both of acoustic waves propagating through thefluid within the pipe and/or pressure disturbances that convect with thefluid flowing in the pipe (e.g., turbulent eddies and vorticaldisturbances), contain useful information regarding parameters of thefluid and the flow process.

Referring to FIG. 1, an apparatus 10 for measuring at least oneparameter associated with a fluid 13 flowing within a pipe 14 is shown.The parameter of the fluid may include, for example, at least one of:velocity of the fluid 13, speed of sound in the fluid 13, density of thefluid 13, volumetric flow rate of the fluid 13, mass flow rate of thefluid 13, composition of the fluid 13, entrained air in the fluid 13,consistency of the fluid 13, and size of particles in the fluid 13. Thefluid 13 may be a single or multiphase fluid flowing through a duct,conduit or other form of pipe 14.

The apparatus 10 includes a spatial array 11 of at least two pressuresensors 15 disposed at different axial locations x₁. . . x_(N) along thepipe 14. Each of the pressure sensors 15 provides a pressure signal P(t)indicative of unsteady pressure within the pipe 14 at a correspondingaxial location x₁. . . x_(N) of the pipe 14. A signal processor 19receives the pressure signals P₁(t) . . . P_(N)(t) from the pressuresensors 15 in the array 11, determines the parameter of the fluid 13using pressure signals from selected ones of the pressure sensors 15,and outputs the parameter as a signal 21. The signal processor 19applies array-processing techniques to the pressure signals P₁(t) . . .P_(N)(t) to determine the velocity, speed of sound of the fluid 13,and/or other parameters of the fluid 13. More specifically, the signalprocessor 19 constructs from the signals at least a portion of a k-ωplot, where the k-ω plot is indicative of a dispersion relation for theunsteady pressure within the pipe. The signal processor 19 thenidentifies a ridge in the k-ω plot. The slope of the ridge is assumed tobe the fluid 13 velocity or sound velocity or correlated to the fluid 13velocity or sound velocity in a known way. Thus, using the slope of theridge, the parameters of the fluid 13 can be determined.

When measuring fluid velocity or speed of sound using array processingtechniques, it is desirable to have a metric that indicates the qualityof the measurement. For example, it is desirable to know if there issufficient signal-to-noise ratio to make a reliable measurement. Also,it is important to have a system check to verify that all components ofthe system 10 are operating properly. The present invention provides aquality metric that can be used to quantitatively evaluate the ridgeidentified in the k-ω plot and, thus, evaluate the fluid 13 velocity orspeed of sound measurement.

FIG. 2 depicts a method used in the apparatus 10 for determining thequality of a ridge identified in the k-ω plane. Referring to FIG. 1 andFIG. 2, this method can be described. After the signal processor 19identifies the ridge in the k-ω plot (block 52), the signal processor 19then determines a quality metric by comparing an accumulated energy(power) of k-ω pairs along the ridge with an accumulated energy (power)of k-ω pairs along at least one ray extending in the k-ω plot (block54). The quality metric is then compared to a threshold value (block56). If the quality metric meets or exceeds the threshold value,indicating a unique ridge resulting from a high signal to noise ratioand proper operation of the device 10, the parameter of the fluid isdetermined using the slope of the ridge (block 58). Conversely, if thequality metric is less than the threshold value, indicating anindistinct ridge resulting from a low signal to noise ratio or improperoperation of the device 10, and an error signal is generated (block 60).The method of FIG. 2 is described in further detail hereinafter.

Using the quality metric, the processor 19 can evaluate the quality ofthe measurement of the velocity of the fluid or the speed of sound. Thequality metric is independent of the interpretation of the velocity orspeed of sound, regardless of whether the velocity or speed of sound isused for determining density of the fluid 13, volumetric flow rate ofthe fluid 13, mass flow rate of the fluid 13, composition of the fluid13, entrained air in the fluid 13, consistency of the fluid 13, and sizeof particles in the fluid 13.

While the apparatus 10 is shown as including four pressure sensors 15,it is contemplated that the array 11 of pressure sensors 15 includes twoor more pressure sensors 15, each providing a pressure signal P(t)indicative of unsteady pressure within the pipe 14 at a correspondingaxial location X of the pipe 14. For example, the apparatus may include2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,22, 23, or 24 pressure sensors 15. Generally, the accuracy of themeasurement improves as the number of sensors in the array increases.The degree of accuracy provided by the greater number of sensors isoffset by the increase in complexity and time for computing the desiredoutput parameter of the flow. Therefore, the number of sensors used isdependent at least on the degree of accuracy desired and the desireupdate rate of the output parameter provided by the apparatus 10.

The signals P₁(t) . . . P_(N)(t) provided by the pressure sensors 15 inthe array 11 are processed by the signal processor 19, which may be partof a larger processing unit 20. For example, the signal processor 19 maybe a microprocessor and the processing unit 20 may be a personalcomputer or other general purpose computer. It is contemplated that thesignal processor 19 may be any one or more analog or digital signalprocessing devices for executing programmed instructions, such as one ormore microprocessors or application specific integrated circuits(ASICS), and may include memory for storing programmed instructions, setpoints, parameters, and for buffering or otherwise storing data.

To determine the one or more parameters 21 of the flow process, thesignal processor 19 applies the data from the selected pressure sensors15 to flow logic 36 executed by signal processor 19. The flow logic 36is described in further detail hereinafter.

The signal processor 19 may output the one or more parameters 21 to adisplay 24 or another input/output (I/O) device 26. The I/O device 26also accepts user input parameters 48 as may be necessary for the flowlogic 36 and diagnostic logic 38. The I/O device 26, display 24, andsignal processor 19 unit may be mounted in a common housing, which maybe attached to the array 11 by a flexible cable, wireless connection, orthe like. The flexible cable may also be used to provide operating powerfrom the processing unit 20 to the array 11 if necessary.

The pressure sensors 15 may include electrical strain gages, opticalfibers and/or gratings, ported sensors, ultrasonic sensors, among othersas described herein, and may be attached to the pipe by adhesive, glue,epoxy, tape or other suitable attachment means to ensure suitablecontact between the sensor and the pipe 14. The sensors 15 mayalternatively be removable or permanently attached via known mechanicaltechniques such as mechanical fastener, spring loaded, clamped, clamshell arrangement, strapping or other equivalents. Alternatively, straingages, including optical fibers and/or gratings, may be embedded in acomposite pipe 14. If desired, for certain applications, gratings may bedetached from (or strain or acoustically isolated from) the pipe 14 ifdesired. It is also within the scope of the present invention that anyother strain sensing technique may be used to measure the variations instrain in the pipe 14, such as highly sensitive piezoelectric,electronic or electric, strain gages attached to or embedded in the pipe14.

In various embodiments of the present invention, a piezo-electronicpressure transducer may be used as one or more of the pressure sensorsand it may measure the unsteady (or dynamic or ac) pressure variationsinside the pipe 14 by measuring the pressure levels inside the pipe. Inone embodiment of the present invention, the sensors 14 comprisepressure sensors manufactured by PCB Piezotronics of Depew, N.Y. Forexample, in one pressure sensor there are integrated circuitpiezoelectric voltage mode-type sensors that feature built-inmicroelectronic amplifiers, and convert the high-impedance charge into alow-impedance voltage output. Specifically, a Model 106B manufactured byPCB Piezotronics is used which is a high sensitivity, accelerationcompensated integrated circuit piezoelectric quartz pressure sensorsuitable for measuring low pressure acoustic phenomena in hydraulic andpneumatic systems. It has the unique capability to measure smallpressure changes of less than 0.001 psi under high static conditions.The 106B has a 300 mV/psi sensitivity and a resolution of 91 dB (0.0001psi).

The pressure sensors 15 may incorporate a built-in MOSFETmicroelectronic amplifier to convert the high-impedance charge outputinto a low-impedance voltage signal. The sensors 15 may be powered froma constant-current source and can operate over long coaxial or ribboncable without signal degradation. The low-impedance voltage signal isnot affected by triboelectric cable noise or insulationresistance-degrading contaminants. Power to operate integrated circuitpiezoelectric sensors generally takes the form of a low-cost, 24 to 27VDC, 2 to 20 mA constant-current supply.

Most piezoelectric pressure sensors are constructed with eithercompression mode quartz crystals preloaded in a rigid housing, orunconstrained tourmaline crystals. These designs give the sensorsmicrosecond response times and resonant frequencies in the hundreds ofkHz, with minimal overshoot or ringing. Small diaphragm diameters ensurespatial resolution of narrow shock waves.

The output characteristic of piezoelectric pressure sensor systems isthat of an AC-coupled system, where repetitive signals decay until thereis an equal area above and below the original base line. As magnitudelevels of the monitored event fluctuate, the output remains stabilizedaround the base line with the positive and negative areas of the curveremaining equal.

Furthermore the present invention contemplates that each of the pressuresensors 15 may include a piezoelectric sensor that provides apiezoelectric material to measure the unsteady pressures of the fluid13. The piezoelectric material, such as the polymer, polarizedfluoropolymer, PVDF, measures the strain induced within the process pipe14 due to unsteady pressure variations within the fluid 13. Strainwithin the pipe 14 is transduced to an output voltage or current by theattached piezoelectric sensors 15.

The PVDF material forming each piezoelectric sensor 15 may be adhered tothe outer surface of a steel strap that extends around and clamps ontothe outer surface of the pipe 14. The piezoelectric sensing element istypically conformal to allow complete or nearly complete circumferentialmeasurement of induced strain. The sensors can be formed from PVDFfilms, co-polymer films, or flexible PZT sensors, similar to thatdescribed in “Piezo Film Sensors technical Manual” provided byMeasurement Specialties, Inc. of Fairfield, N.J., which is incorporatedherein by reference. The advantages of this technique are the following:

1. Non-intrusive flow rate measurements

2. Low cost

3. Measurement technique requires no excitation source. Ambient flownoise is used as a source.

4. Flexible piezoelectric sensors can be mounted in a variety ofconfigurations to enhance signal detection schemes. These configurationsinclude a) co-located sensors, b) segmented sensors with opposingpolarity configurations, c) wide sensors to enhance acoustic signaldetection and minimize vortical noise detection, d) tailored sensorgeometries to minimize sensitivity to pipe modes, e) differencing ofsensors to eliminate acoustic noise from vortical signals.

5. Higher Temperatures (140C) (co-polymers)

Flow Logic

Velocity Processing

Referring to FIG. 3, an example of flow logic 36 is shown. As previouslydescribed, the array 11 of at least two sensors 15 located at twolocations x₁,x₂ axially along the pipe 14 sense respective stochasticsignals propagating between the sensors 15 within the pipe 14 at theirrespective locations. Each sensor 15 provides a signal indicating anunsteady pressure at the location of each sensor 15, at each instant ina series of sampling instants. One will appreciate that the array 11 mayinclude more than two sensors 15 distributed at locations x₁. . . x_(N).The pressure generated by the convective pressure disturbances (e.g.,eddies 120, see FIG. 4) may be measured through strained-based sensors15 and/or pressure sensors 15. The sensors 15 provide analog pressuretime-varying signals P₁(t),P₂(t),P₃(t) . . . P_(N)(t) to the signalprocessor 19, which in turn applies selected ones of these signalsP₁(t),P₂(t),P₃(t), . . . P_(N)(t) to the flow logic 36.

The flow logic 36 processes the selected signals P₁(t),P₂(t),P₃(t), . .. P_(N)(t) to first provide output signals (parameters) 21 indicative ofthe pressure disturbances that convect with the fluid (process flow) 13,and subsequently, provide output signals (parameters) 21 in response topressure disturbances generated by convective waves propagating throughthe fluid 13, such as velocity, Mach number and volumetric flow rate ofthe process flow 13.

The signal processor 19 includes data acquisition unit 126 (e.g., A/Dconverter) that converts the analog signals P₁(t) . . . P_(N)(t) torespective digital signals and provides the digital signals P₁(t) . . .P_(N)(t) to FFT logic 128. The FFT logic 128 calculates the Fouriertransform of the digitized time-based input signals P₁(t) . . . P_(N)(t)and provides complex frequency domain (or frequency based) signalsP₁(ω),P₂(ω),P₃(ω), . . . P_(N)(ω) indicative of the frequency content ofthe input signals. Instead of FFT's, any other technique for obtainingthe frequency domain characteristics of the signals P₁(t)-P_(N)(t), maybe used. For example, the cross-spectral density and the power spectraldensity may be used to form a frequency domain transfer functions (orfrequency response or ratios) discussed hereinafter.

One technique of determining the convection velocity of the turbulenteddies 120 within the process flow 13 is by characterizing a convectiveridge of the resulting unsteady pressures using an array of sensors orother beam forming techniques, similar to that described in U.S. Pat.No. 6,691,584, filed on Jul. 2, 1999 and U.S. Pat. No. 6,609,069, filedon Dec. 4, 2000, which are incorporated herein by reference.

A data accumulator 130 accumulates the frequency signals P₁(ω)-P_(N)(ω)over a sampling interval, and provides the data to an array processor132, which performs a spatial-temporal (two-dimensional) transform ofthe sensor data, from the xt domain to the k-ω domain, and thencalculates the power in the k-ω plane, as represented by a k-ω plot.

The array processor 132 uses standard so-called beam forming, arrayprocessing, or adaptive array-processing algorithms, i.e. algorithms forprocessing the sensor signals using various delays and weighting tocreate suitable phase relationships between the signals provided by thedifferent sensors, thereby creating phased antenna array functionality.In other words, the beam forming or array processing algorithmstransform the time domain signals from the sensor array into theirspatial and temporal frequency components, i.e. into a set of wavenumbers given by k=2π/λ where λ is the wavelength of a spectralcomponent, and corresponding angular frequencies given by ω=2πν.

The prior art teaches many algorithms of use in spatially and temporallydecomposing a signal from a phased array of sensors, and the presentinvention is not restricted to any particular algorithm. One particularadaptive array processing algorithm is the Capon method/algorithm. Whilethe Capon method is described as one method, the present inventioncontemplates the use of other adaptive array processing algorithms, suchas MUSIC algorithm. The present invention recognizes that suchtechniques can be used to determine flow rate, i.e. that the signalscaused by a stochastic parameter convecting with a flow are timestationary and have a coherence length long enough that it is practicalto locate sensor units apart from each other and yet still be within thecoherence length.

Convective characteristics or parameters have a dispersion relationshipthat can be approximated by the straight-line equation,k=ω/u,where u is the convection velocity (flow velocity). A plot of k-ω pairsobtained from a spectral analysis of sensor samples associated withconvective parameters portrayed so that the energy of the disturbancespectrally corresponding to pairings that might be described as asubstantially straight ridge, a ridge that in turbulent boundary layertheory is called a convective ridge. What is being sensed are notdiscrete events of turbulent eddies, but rather a continuum of possiblyoverlapping events forming a temporally stationary, essentially whiteprocess over the frequency range of interest. In other words, theconvective eddies 120 is distributed over a range of length scales andhence temporal frequencies.

To calculate the power in the k-ω plane, as represented by a k-ω plot(see FIG. 5) of either the signals, the array processor 132 determinesthe wavelength and so the (spatial) wavenumber k, and also the(temporal) frequency and so the angular frequency ω, of various of thespectral components of the stochastic parameter. There are numerousalgorithms available in the public domain to perform thespatial/temporal decomposition of arrays of sensors 15.

The present invention may use temporal and spatial filtering toprecondition the signals to effectively filter out the common modecharacteristics Pcommon mode and other long wavelength (compared to thesensor spacing) characteristics in the pipe 14 by differencing adjacentsensors 15 and retain a substantial portion of the stochastic parameterassociated with the flow field and any other short wavelength (comparedto the sensor spacing) low frequency stochastic parameters.

In the case of suitable turbulent eddies 120 (see FIG. 4) being present,the power in the k-ω plane shown in a k-ω plot of FIG. 5 shows aconvective ridge 124. The convective ridge represents the concentrationof a stochastic parameter that convects with the flow and is amathematical manifestation of the relationship between the spatialvariations and temporal variations described above. Such a plot willindicate a tendency for k-ω pairs to appear more or less along a line124 with some slope, the slope indicating the flow velocity.

Once the power in the k-ω plane is determined, a convective ridgeidentifier 134 uses one or another feature extraction method todetermine the location and orientation (slope) of any convective ridge124 present in the k-ω plane. In one embodiment, the convective ridgeidentifier 134 accumulates energy (power) of k-ω pairs in the k-ω plotalong different rays emanating from the origin, each different ray beingassociated with a different trial velocity (in that the slope of a rayis assumed to be the fluid 13 velocity or correlated to the fluid 13velocity in a known way). The convective ridge identifier 134 mayaccumulate energy for each array by summing the energy of k-ω pairsalong the ray. Alternatively, other methods of accumulating energy alongthe ray (e.g., averaging) may be used. In any case, accumulated energyis determined for a range of trial velocities between a predeterminedminimum velocity and a predetermined maximum velocity. The convectiveridge has an orientation that is the slope of the ray having the largestaccumulated energy. The convective ridge identifier 134 providesinformation about the different trial velocities, information referredto generally as convective ridge information.

FIG. 6 depicts an example of a plot of accumulated energy for trialvelocities ranging from about 4.5 ft/sec to about 30 ft/sec, whereaccumulated energy is indicated as power in decibels (dB) and the trialvelocities are indicated in feet per second (ft/sec). In FIG. 6, thelargest accumulated energy is approximately −37 dB, so the best velocity(i.e., the velocity indicated by the convective ridge) is approximately6 ft/sec. The convective ridge identifier 134 may determine the bestvelocity using any known iterative routine, curve fit routine or otherroutine to identify the portion of the curve indicating the largestaccumulated energy.

Once the convective ridge is identified in the k-ω plot, the quality ofthis ridge can be determined using the method of FIG. 2. As shown inFIG. 2 at block 54, the signal processor 19 determines a quality metricby comparing an accumulated energy (power) of k-ω pairs along the ridgewith an accumulated energy (power) of k-ω pairs along at least one rayextending in the k-ω plot (block 54). In other words, the quality metricis determined by comparing the accumulated energy at the best velocity(P_(best velocity)) to a reference accumulated energy (P_(reference)),which is determined as a function of one or more trial velocities. Forexample, P_(reference) may be an average of accumulated energies for arange of trial velocities. Alternatively, P_(reference) may bedetermined as a function of a single trial velocity (a referencevelocity). The reference velocity may be a predetermined velocity, suchas the maximum or minimum velocity, or may be determined as a functionof the best velocity (e.g., 75% of the best velocity, 50% of the bestvelocity, etc.).

In one embodiment, the reference velocity is selected by determining theaccumulated energy for a plurality of different velocities and selectingthe reference velocity as that velocity providing the maximumaccumulated energy. For example, the quality metric algorithm may use areference velocity determined from the maximum of one of the followingfour values: 1) accumulated energy at 75% of best velocity, 2)accumulated energy at 125% of best velocity, 3) accumulated energy atminimum velocity and 4) accumulated energy at maximum velocity, althoughit is not necessarily limited to these. In the example of FIG. 6, thesevelocities equate to 4.5, 7.5, 3 and 30 ft/sec, respectively, with thecorresponding accumulated energies being −51 dB, −49 dB, −48 dB and−49.5 dB, respectively. Therefore, the reference velocity is selected as3 ft/sec (minimum velocity), with a corresponding accumulated energybeing −48 dB. While the present embodiment includes four points fordetermining the accumulated energy of the reference velocity, theinvention contemplates that any number of points or point locations maybe used.

After the accumulated energy at the best velocity (P_(best velocity))and reference accumulated energy (P_(reference)) are determined, theyare then converted from the dB scale to a linear scale [10{circumflexover ( )}(dB/10)=linear output]. The quality metric may then becalculated by dividing the difference of P_(best velocity) andP_(reference) by the sum of P_(best velocity) and P_(reference), asshown by the equation below.$Q = \frac{P_{{Best}\quad{Velocity}} - P_{Reference}}{P_{{Best}\quad{Velocity}} + P_{Reference}}$

If P_(best velocity) is much bigger than P_(reference), indicating asharp, unique convective ridge resulting from a high signal to noiseratio and proper operation of the device 10 (FIG. 1), the quality metricwill approach one. Conversely, if P_(best velocity) and P_(reference)are equal, indicating an indistinct convective ridge resulting from alow signal to noise ratio or improper operation of the device 10, thequality metric will equal zero. Therefore, the processor can evaluatethe quality of the convective ridge using the quality metric. If thequality metric is below a predetermined threshold, the apparatus 10 willprovide an error (blocks 56 and 60 of FIG. 2). For example, a thresholdof about 0.2 may be used, but this threshold may vary depending upon theenvironment in which the array 11 (FIG. 1) is located.

If the quality metric is greater than or equal to the threshold (block56 of FIG. 2), there is a level of confidence the device 10 is operatingproperly and the fluid 13 velocity may be determined using the slope ofthe convective ridge (blocks 56 and 58 of FIG. 2). In this case, theanalyzer 136 examines the convective ridge information including theconvective ridge orientation (slope). Assuming the straight-linedispersion relation given by k=ω/u, the analyzer 136 determines the flowvelocity, Mach number and/or volumetric flow, which are output asparameters 21. The volumetric flow is determined by multiplying thecross-sectional area of the inside of the pipe with the velocity of theprocess flow.

Some or all of the functions within the flow logic 36 may be implementedin software (using a microprocessor or computer) and/or firmware, or maybe implemented using analog and/or digital hardware, having sufficientmemory, interfaces, and capacity to perform the functions describedherein.

Speed of Sound (SOS) Processing

Referring to FIG. 7, another example of flow logic 36 is shown. Whilethe examples of FIG. 3 and FIG. 7 are shown separately, it iscontemplated that the flow logic 36 may perform all of the functionsdescribed with reference to FIG. 3 and FIG. 7. As previously described,the array 11 of at least two sensors 15 located at two at least twolocations x1,x2 axially along the pipe 14 sense respective stochasticsignals propagating between the sensors within the pipe at theirrespective locations. Each sensor 15 provides a signal indicating anunsteady pressure at the location of each sensor 15, at each instant ina series of sampling instants. One will appreciate that the sensor array11 may include more than two pressure sensors 15 distributed atlocations x₁. . . X_(N). The pressure generated by the acoustic pressuredisturbances (e.g., acoustic waves 122, see FIG. 4) may be measuredthrough strained-based sensors and/or pressure sensors. The sensors 15provide analog pressure time-varying signals P₁(t),P₂(t),P₃(t), . . .P_(N)(t) to the flow logic 36. The flow logic 36 processes the signalsP₁(t),P₂(t),P₃(t), . . . P_(N)(t) from the sensors 15 to first provideoutput signals indicative of the speed of sound propagating through thefluid (process flow) 13, and subsequently, provide output signals inresponse to pressure disturbances generated by acoustic wavespropagating through the process flow 13, such as velocity, Mach numberand volumetric flow rate of the process flow 13.

The signal processor 19 receives the pressure signals from the array 11of sensors 15. A data acquisition unit 138 digitizes selected ones ofthe pressure signals P₁(t) . . . P_(N)(t) associated with the acousticwaves 122 propagating through the pipe 14. Similarly to the FFT logic128 of FIG. 3, an FFT logic 140 calculates the Fourier transform of theselected digitized time-based input signals P₁(t) . . . P_(N)(t) andprovides complex frequency domain (or frequency based) signalsP₁(ω),P₂(ω),P₃(ω), . . . P_(N)(ω) indicative of the frequency content ofthe input signals.

A data accumulator 142 accumulates the frequency signals P₁(ω) . . .P_(N)(ω) over a sampling interval, and provides the data to an arrayprocessor 144, which performs a spatial-temporal (two-dimensional)transform of the sensor data, from the xt domain to the k-ω domain, andthen calculates the power in the k-ω plane, as represented by a k-ωplot.

To calculate the power in the k-ω plane, as represented by a k-ω plot(see FIG. 8) of either the signals or the differenced signals, the arrayprocessor 144 determines the wavelength and so the (spatial) wavenumberk, and also the (temporal) frequency and so the angular frequency ω, ofvarious of the spectral components of the stochastic parameter. Thereare numerous algorithms available in the public domain to perform thespatial/temporal decomposition of arrays of sensor units 15.

In the case of suitable acoustic waves 122 being present in both axialdirections, the power in the k-ω plane shown in a k-ω plot of FIG. 8 sodetermined will exhibit a structure that is called an acoustic ridge150, 152 in both the left and right planes of the plot, wherein one ofthe acoustic ridges 150 is indicative of the speed of sound traveling inone axial direction and the other acoustic ridge 152 being indicative ofthe speed of sound traveling in the other axial direction. The acousticridges represent the concentration of a stochastic parameter thatpropagates through the flow and is a mathematical manifestation of therelationship between the spatial variations and temporal variationsdescribed above. Such a plot will indicate a tendency for k-ω pairs toappear more or less along a line 150, 152 with some slope, the slopeindicating the speed of sound.

The power in the k-ω plane so determined is then provided to an acousticridge identifier 146, which uses one or another feature extractionmethod to determine the location and orientation (slope) of any acousticridge present in the left and/or right k-ω plane. The velocity may bedetermined by using the slope of one of the two acoustic ridges 150, 152or averaging the slopes of the acoustic ridges 150, 152.

In one embodiment, the acoustic ridge identifier 146 accumulates energy(power) of k-ω pairs in the k-ω plot along different rays emanating fromthe origin, each different ray being associated with a different trialvelocity (in that the slope of a ray is assumed to be the sound velocityor correlated to the sound velocity in a known way). The acoustic ridgeidentifier 146 may accumulate energy for each ray by summing theenergies of k-ω pairs along the ray. Alternatively, other methods ofaccumulating energy along the ray (e.g., averaging) may be used. In anycase, accumulated energy is determined for a range of trial velocitiesbetween a predetermined minimum velocity and a predetermined maximumvelocity. The convective ridges 150, 152 may be identified by the rayhaving the largest accumulated energy in the respective plane of the k-ωplot. The acoustic ridge identifier 146 provides information about thedifferent trial velocities, information referred to generally asacoustic ridge information.

FIG. 9 depicts an example of a plot of accumulated energy for trialvelocities ranging from about 713 ft/sec to about 5000 ft/sec, whereaccumulated energy is indicated as power in decibels (dB) and the trialvelocities are indicated in feet per second (ft/sec). The accumulatedenergy may be a sum of the powers associated with k-ω pairs along asingle ray (e.g., a ray in the right plane or the left plane of the k-ωplot) or may be a sum of the powers associated with k-ω pairs along raysof corresponding slope in both the right and left planes of the k-ωplot.

In FIG. 9, the largest accumulated energy is approximately −53 dB, sothe best velocity (i.e., the velocity indicated by the acoustic ridges)is approximately 950 ft/sec. The acoustic ridge identifier 146 maydetermine the best velocity using any known iterative routine, curve fitroutine or other routine to identify the portion of the curve indicatingthe largest accumulated energy.

After at least one of the acoustic ridges 150, 152 is identified in thek-ω plot, the quality of the at least one ridge can be determined usingthe method of FIG. 2. As shown in FIG. 2 at block 54, the signalprocessor 19 determines a quality metric by comparing an accumulatedenergy (power) of k-ω pairs along the at least one ridge with anaccumulated energy (power) of k-ω pairs along at least one ray extendingin the k-ω plot (block 54). In other words, the quality of themeasurement is determined by comparing the accumulated energy at thebest velocity (P_(best velocity)) to a reference accumulated energy(P_(reference)), which is determined as a function of one or more trialvelocities. For example, P_(reference) may be an average of accumulatedenergies for a range of trial velocities or for corresponding trialvelocities in the right and left planes of the k-ω plot. Alternatively,P_(reference) may be determined as a function of a single trial velocity(a reference velocity). The reference velocity may be a predeterminedvelocity, such as the maximum or minimum velocity, or may be determinedas a function of the best velocity (e.g., 75% of the best velocity, 50%of the best velocity, etc.).

In one embodiment, the reference velocity is selected by determining theaccumulated energy for a plurality of different velocities and selectingthe reference velocity as that velocity providing the maximumaccumulated energy. For example, the quality metric algorithm may use areference velocity determined from the maximum of one of the followingfour values: 1) accumulated energy at 75% of best velocity, 2)accumulated energy at 125% of best velocity, 3) accumulated energy atminimum velocity and 4) accumulated energy at maximum velocity, althoughit is not necessarily limited to these. In the example of FIG. 9, thesevelocities equate to 713, 1188, 100 and 5000 ft/sec, respectively, withthe corresponding accumulated energies being −57 dB, −54 dB, −78 dB and−58 dB, respectively. Therefore, the reference velocity is selected as1188 ft/sec (125% of best velocity), with a corresponding accumulatedenergy being −54 dB. While the present embodiment includes four pointsfor determining the accumulated energy of the reference velocity, theinvention contemplates that any number of points or point locations maybe used.

After the accumulated energy at the best velocity (P_(best velocity))and reference accumulated energy (P_(reference)) are determined, theyare then converted from the dB scale to a linear scale [10{circumflexover ( )}(dB/10)=linear output]. The quality metric may then becalculated by dividing the difference of P_(best velocity) andP_(reference) by the sum of P_(best velocity) and P_(reference), asshown by the equation below.$Q = \frac{P_{{BEST}\quad{VELOCITY}} - P_{REFERNCE}}{P_{{BEST}\quad{VELOCITY}} + P_{REFERNCE}}$

If P_(best velocity) is much bigger than P_(reference), indicating asharp, unique acoustic ridge resulting from a high signal to noise ratioand proper operation of the device 10 (FIG. 1), the quality metric willapproach one. Conversely, if P_(best velocity) and P_(reference) areequal, indicating an indistinct acoustic ridge resulting from a lowsignal to noise ratio or improper operation of the device 10, thequality metric will equal zero. Therefore, the processor can evaluatethe quality of the acoustic ridge(s) using the quality metric. If thequality metric is below a predetermined threshold, the apparatus 10 willprovide an error (blocks 56 and 60 of FIG. 2). For example, a thresholdof about 0.2 may be used, but this threshold may vary depending upon theenvironment in which the array 11 (FIG. 1) is located.

If the quality metric is greater than or equal to the threshold (block56 of FIG. 2), there is a level of confidence the device 10 is operatingproperly and the speed of sound may be determined using the slope of theacoustic ridge(s) (blocks 56 and 58 of FIG. 2). In this case,information including the acoustic ridge orientation (slope) is used byan analyzer 148 to determine the flow parameters relating to measuredspeed of sound, such as the consistency or composition of the flow, thedensity of the flow, the average size of particles in the flow, theair/mass ratio of the flow, gas volume fraction of the flow, the speedof sound propagating through the flow, and/or the percentage ofentrained air within the flow.

Similar to the array processor 132 of FIG. 3, the array processor 144uses standard so-called beam forming, array processing, or adaptivearray-processing algorithms, i.e. algorithms for processing the sensorsignals using various delays and weighting to create suitable phaserelationships between the signals provided by the different sensors,thereby creating phased antenna array functionality. In other words, thebeam forming or array processing algorithms transform the time domainsignals from the sensor array into their spatial and temporal frequencycomponents, i.e. into a set of wave numbers given by k=2π/λ where λ isthe wavelength of a spectral component, and corresponding angularfrequencies given by ω=2πν.

One such technique of determining the speed of sound propagating throughthe process flow 13 is using array processing techniques to define anacoustic ridge in the k-ω plane as shown in FIG. 8. The slope of theacoustic ridge is indicative of the speed of sound propagating throughthe process flow 13. The speed of sound (SOS) is determined by applyingsonar arraying processing techniques to determine the speed at which theone dimensional acoustic waves propagate past the axial array ofunsteady pressure measurements distributed along the pipe 14.

The flow logic 36 of the present embodiment measures the speed of sound(SOS) of one-dimensional sound waves propagating through the processflow 13 to determine the gas volume fraction of the process flow 13. Itis known that sound propagates through various mediums at various speedsin such fields as SONAR and RADAR fields. The speed of sound propagatingthrough the pipe 14 and process flow 13 may be determined using a numberof known techniques, such as those set forth in U.S. patent applicationSer. No. 09/344,094, filed Jun. 25, 1999, now U.S. Pat. No. 6,354,147;U.S. patent application Ser. No. 10/795,111, filed Mar. 4, 2004; U.S.patent application Ser. No. 09/997,221, filed Nov. 28, 2001, now U.S.Pat. No. 6,587,798; U.S. patent application Ser. No. 10/007,749, filedNov. 7, 2001, and U.S. patent application Ser. No. 10/762,410, filedJan. 21, 2004, each of which are incorporated herein by reference.

While the sonar-based flow meter using an array of sensors 15-18 tomeasure the speed of sound of an acoustic wave propagating through themixture is shown and described, one will appreciate that any means formeasuring the speed of sound of the acoustic wave may used to determinethe entrained gas volume fraction of the mixture/fluid or othercharacteristics of the flow described hereinbefore.

The analyzer 148 of the flow logic 36 provides output parameters 21indicative of characteristics of the process flow 13 that are related tothe measured speed of sound (SOS) propagating through the process flow13. For example, to determine the gas volume fraction (or phasefraction), the analyzer 148 assumes a nearly isothermal condition forthe process flow 13. As such the gas volume fraction or the voidfraction is related to the speed of sound by the following quadraticequation:Ax ² +Bx+C=0wherein x is the speed of sound, A=1+rg/r1*(K_(eff)/P−1)−K_(eff)/P,B=K_(eff)/P−2+rg/r1; C=1−K_(eff)/r1*a_(meas{circumflex over ( )})2);Rg=gas density, r1=liquid density, K_(eff)=effective K (modulus of theliquid and pipewall), P=pressure, and a_(meas)=measured speed of sound.

Effectively,Gas Voulume Fraction (GVF)=(−B+sqrt(B{circumflex over( )}2-4*A*C))/(2*A)

Alternatively, the sound speed of a mixture can be related to volumetricphase fraction (□_(i)) of the components and the sound speed (a) anddensities (ρ) of the component through the Wood equation.$\frac{1}{\rho_{mix}a_{{mix}_{\infty}}^{2}} = {{\sum\limits_{i = 1}^{N}{\frac{\phi_{i}}{\rho_{i}a_{i}^{2}}{~~~}{where}\quad\rho_{mix}}} = {\sum\limits_{i = 1}^{N}{\rho_{i}\phi_{i}}}}$

One dimensional compression waves propagating within a process flow 13contained within a pipe 14 exert an unsteady internal pressure loadingon the pipe. The degree to which the pipe displaces as a result of theunsteady pressure loading influences the speed of propagation of thecompression wave. The relationship among the infinite domain speed ofsound and density of a mixture; the elastic modulus (E), thickness (t),and radius (R) of a vacuum-backed cylindrical conduit; and the effectivepropagation velocity (aeff) for one dimensional compression is given bythe following expression: $\begin{matrix}{a_{eff} = \frac{1}{\sqrt{{1/a_{{mix}_{\infty}}^{2}} + {\rho_{mix}\frac{2R}{Et}}}}} & \left( {{eq}\quad 1} \right)\end{matrix}$

The mixing rule essentially states that the compressibility of a processflow (1/(□a²)) is the volumetrically-weighted average of thecompressibilities of the components. For a process flow 13 consisting ofa gas/liquid mixture at pressure and temperatures typical of paper andpulp industry, the compressibility of gas phase is orders of magnitudesgreater than that of the liquid. Thus, the compressibility of the gasphase and the density of the liquid phase primarily determine mixturesound speed, and as such, it is necessary to have a good estimate ofprocess pressure to interpret mixture sound speed in terms of volumetricfraction of entrained gas. The effect of process pressure on therelationship between sound speed and entrained air volume fraction isshown in FIG. 10.

As described hereinbefore, the flow logic 36 of the present embodimentincludes the ability to accurately determine the average particle sizeof a particle/air or droplet/air mixture within the pipe 14 and the airto particle ratio. Provided there is no appreciable slip between the airand the solid coal particle, the propagation of one dimensional soundwave through multiphase mixtures is influenced by the effective mass andthe effective compressibility of the mixture. For an air transportsystem, the degree to which the no-slip assumption applies is a strongfunction of particle size and frequency. In the limit of small particlesand low frequency, the no-slip assumption is valid. As the size of theparticles increases and the frequency of the sound waves increase, thenon-slip assumption becomes increasing less valid. For a given averageparticle size, the increase in slip with frequency causes dispersion,or, in other words, the sound speed of the mixture to change withfrequency. With appropriate calibration the dispersive characteristic ofa process flow 13 will provide a measurement of the average particlesize, as well as, the air to particle ratio (particle/fluid ratio) ofthe process flow 13.

In accordance with the present invention the dispersive nature of thesystem utilizes a first principles model of the interaction between theair and particles. This model is viewed as being representative of aclass of models that seek to account for dispersive effects. Othermodels could be used to account for dispersive effects without alteringthe intent of this disclosure (for example, see the paper titled“Viscous Attenuation of Acoustic Waves in Suspensions” by R. L. Gibson,Jr. and M. N. Toksoz), which is incorporated herein by reference. Themodel allows for slip between the local velocity of the continuous fluidphase and that of the particles.

The following relation can be derived for the dispersive behavior of anidealized fluid particle mixture.${a_{mix}(\omega)} = {a_{f}\sqrt{\frac{1}{1 + \frac{\varphi_{p}\rho_{p}}{\rho_{f}\left( {1 + {\omega^{2}\frac{\rho_{p}^{2}v_{p}^{2}}{K^{2}}}} \right)}}}}$

In the above relation, the fluid SOS, density (ρ) and viscosity (φ) arethose of the pure phase fluid, v_(p) is the volume of individualparticles and ρ_(p) is the volumetric phase fraction of the particles inthe mixture.

Two parameters of particular interest in steam processes andair-conveyed particles processes are particle size and air-to-fuel massratio or steam quality. To this end, it is of interest to examine thedispersive characteristics of the mixture as a function of these twovariables. FIG. 11 and FIG. 12 show the dispersive behavior in relationsto the speed of sound for coal/air mixtures with parameters typical ofthose used in pulverized coal deliver systems.

In particular FIG. 11 shows the predicted behavior for nominally 50micrometer size coal in air for a range of air-to-fuel ratios. As shown,the effect of air-to-fuel ratio is well defined in the low frequencylimit. However, the effect of the air-to-fuel ratio becomesindistinguishable at higher frequencies, approaching the sound speed ofthe pure air at high frequencies (above ˜100 Hz).

Similarly, FIG. 12 shows the predicted behavior for a coal/air mixturewith an air-to-fuel ratio of 1.8 with varying particle size. This figureillustrates that particle size has no influence on either the lowfrequency limit (quasi-steady) sound speed, or on the high frequencylimit of the sound speed. However, particle size does have a pronouncedeffect in the transition region.

FIG. 11 and FIG. 12 illustrate an important aspect of the presentinvention. Namely, that the dispersive properties of dilute mixtures ofparticles suspended in a continuous liquid can be broadly classifiedinto three frequency regimes: low frequency range, high frequency rangeand a transitional frequency range. Although the effect of particle sizeand air-to-fuel ratio are inter-related, the predominant effect ofair-to-fuel ratio is to determine the low frequency limit of the soundspeed to be measured and the predominate effect of particle size is todetermine the frequency range of the transitional regions. As particlesize increases, the frequency at which the dispersive properties appeardecreases. For typical pulverized coal applications, this transitionalregion begins at fairly low frequencies, ˜2Hz for 50 micrometer sizeparticles.

Given the difficulties measuring sufficiently low frequencies to applythe quasi-steady model and recognizing that the high frequency soundspeed contains no direct information on either particle size orair-to-fuel ratio, it becomes apparent that the dispersivecharacteristics of the coal/air mixture should be utilized to determineparticle size and air-to-fuel ratio based on speed of soundmeasurements.

Some or all of the functions within the flow logic 36 may be implementedin software (using a microprocessor or computer) and/or firmware, or maybe implemented using analog and/or digital hardware, having sufficientmemory, interfaces, and capacity to perform the functions describedherein.

While FIG. 3 and FIG. 7 depict two different embodiments of the flowlogic 36 to measure various parameters of the flow process, the presentinvention contemplates that the functions of these two embodiments maybe performed by a single flow logic 36.

It should be understood that any of the features, characteristics,alternatives or modifications described regarding a particularembodiment herein may also be applied, used, or incorporated with anyother embodiment described herein.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

The present invention can be embodied in the form ofcomputer-implemented processes and apparatuses for practicing thoseprocesses. The present invention can also be embodied in the form ofcomputer program code containing instructions embodied in tangiblemedia, such as floppy diskettes, CD-ROMs, hard drives, or any othercomputer-readable storage medium, wherein, when the computer programcode is loaded into and executed by a computer, the computer becomes anapparatus for practicing the invention. The present invention can alsobe embodied in the form of computer program code, for example, whetherstored in a storage medium, loaded into and/or executed by a computer,or transmitted over some transmission medium, such as over electricalwiring or cabling, through fiber optics, or via electromagneticradiation, wherein, when the computer program code is loaded into andexecuted by a computer, the computer becomes an apparatus for practicingthe invention. When implemented on a general-purpose microprocessor, thecomputer program code segments configure the microprocessor to createspecific logic circuits.

It should be understood that any of the features, characteristics,alternatives or modifications described regarding a particularembodiment herein may also be applied, used, or incorporated with anyother embodiment described herein.

Although the invention has been described and illustrated with respectto exemplary embodiments thereof, the foregoing and various otheradditions and omissions may be made therein and thereto withoutdeparting from the spirit and scope of the present invention.

1. An apparatus for measuring a parameter of a fluid passing through apipe, the apparatus comprising: a spatial array of at least two sensorsdisposed at different axial locations along the pipe, each of thesensors providing a signal indicative of unsteady pressure within thepipe at a corresponding axial location of the pipe; and a signalprocessor configured to: construct from the signals at least a portionof a k-ω plot, where the k-ω plot is indicative of a dispersion relationfor the unsteady pressure within the pipe, detect at least one ridge inthe k-ω plot, a slope of the at least one ridge being indicative of theparameter of the fluid, and compare an accumulated energy for k-ω pairsalong the at least one ridge with an accumulated energy for k-ω pairsalong at least one ray extending in the k-ω plot to determine a qualitymetric indicative of a quality of the at least one ridge.
 2. Theapparatus of claim 1, wherein the accumulated energy for k-ω pairs alongthe at least one ridge is a sum of the powers associated with the k-ωpairs along the at least one ridge.
 3. The apparatus of claim 1, whereinthe accumulated energy for k-ω pairs along the at least one ray is a sumof the powers associated with the k-ω pairs along the at least one ray.4. The apparatus of claim 1, wherein the accumulated energy for k-ωpairs along the at least one ray is an average accumulated energy fork-ω pairs along a plurality of rays.
 5. The apparatus of claim 1,wherein the at least one ray has a slope indicative of a referencevelocity.
 6. The apparatus of claim 5, wherein the slope of the at leastone ridge is indicative of a best velocity, and the reference velocityis determined as a function of the best velocity.
 7. The apparatus ofclaim 5, wherein the slope of the at least one ridge is indicative of abest velocity, and the reference velocity is independent of the bestvelocity.
 8. The apparatus of claim 5, wherein the signal processor isfurther configured to: determine accumulated energies for a plurality ofrays in the k-ω plot, the slopes of the plurality of rays indicating aplurality of trial velocities, and select the reference velocity fromthe trial velocities by comparing the accumulated energies for theplurality of rays.
 9. The apparatus of claim 8, wherein the slope of theat least one ridge is indicative of a best velocity, and the trialvelocities include: a trial velocity determined as a function of thebest velocity and a trial velocity independent of the best velocity. 10.The apparatus of claim 8, wherein the slope of the at least one ridge isindicative of a best velocity, and the signal processor determines thequality metric using:$Q = \frac{P_{{BEST}\quad{VELOCITY}} - P_{REFERNCE}}{P_{{BEST}\quad{VELOCITY}} + P_{REFERNCE}}$where P_(best velocity) is the accumulated energy for k-ω pairs alongthe at least one ridge in a linear scale, P_(reference) is theaccumulated energy for k-ω pairs along the at least one ray in a linearscale, and Q is the quality metric.
 11. The apparatus of claim 1,wherein the slope of the at least one ridge is indicative of a bestvelocity, and the signal processor determines the quality metric using:$Q = \frac{P_{{BEST}\quad{VELOCITY}} - P_{REFERNCE}}{P_{{BEST}\quad{VELOCITY}} + P_{REFERNCE}}$where P_(best velocity) is the accumulated energy for k-ω pairs alongthe at least one ridge in a linear scale, P_(reference) is theaccumulated energy for k-ω pairs along the at least one ray in a linearscale, and Q is the quality metric.
 12. The apparatus of claim 1,wherein the at least one ridge includes a first acoustic ridge in a leftplane of the k-ω plot and a second acoustic ridge in the right plane ofthe k-ω plot, and the accumulated energy for k-ω pairs along the atleast one ridge is a sum of the powers associated with the k-ω pairsalong the first and second acoustic ridges.
 13. The apparatus of claim1, wherein the parameter of the fluid includes at least one of: velocityof the fluid and speed of sound of the fluid.
 14. The apparatus of claim1 wherein the at least two pressure sensors are selected from a groupconsisting of: piezoelectric, piezoresistive, strain gauge, PVDF,optical sensors, ported ac pressure sensors, accelerometers, velocitysensors, and displacement sensors.
 15. The apparatus of claim 1, whereinthe at least two pressure sensors are wrapped around at least a portionof the pipe and do not contact the fluid.
 16. The apparatus of claim 1,wherein the signal processor is further configured to compare thequality metric to a threshold value; and determine the parameter of thefluid using the slope of the at least one ridge in response to thequality metric reaching the threshold value.
 17. A method fordetermining a quality metric of a measurement of a parameter of a fluidflowing through a pipe, the measurement being made using a spatial arrayof at least two sensors disposed at different axial locations along thepipe, each of the sensors providing a signal indicative of unsteadypressure within the pipe at a corresponding axial location of the pipe,the method comprising: constructing from the signals at least a portionof a k-ω plot, where the k-ω plot is indicative of a dispersion relationfor the unsteady pressure within the pipe; detecting at least one ridgein the k-ω plot, a slope of the at least one ridge being indicative ofthe parameter of the fluid; comparing an accumulated energy for k-ωpairs along the at least one ridge with an accumulated energy for k-ωpairs along at least one ray extending in the k-ω plot to determine aquality metric indicative of a quality of the at least one ridge. 18.The method of claim 17, wherein the accumulated energy for k-ω pairsalong the at least one ridge is a sum of the powers associated with thek-ω pairs along the at least one ridge.
 19. The method of claim 17,wherein the accumulated energy for k-ω pairs along the at least one rayis a sum of the powers associated with the k-ω pairs along the at leastone ray.
 20. The method of claim 17, wherein the accumulated energy fork-ω pairs along the at least one ray is an average accumulated energyfor k-ω pairs along a plurality of rays.
 21. The method of claim 17,wherein the at least one ray has a slope indicative of a referencevelocity.
 22. The method of claim 21, wherein the slope of the at leastone ridge is indicative of a best velocity, and the reference velocityis determined as a function of the best velocity.
 23. The method ofclaim 21, wherein the slope of the at least one ridge is indicative of abest velocity, and the reference velocity is independent of the bestvelocity.
 24. The method of claim 21, further comprising: determiningaccumulated energies for a plurality of rays in the k-ω plot, the slopesof the plurality of rays indicating a plurality of trial velocities, andselecting the reference velocity from the trial velocities by comparingthe accumulated energies for the plurality of rays.
 25. The method ofclaim 24, wherein the slope of the at least one ridge is indicative of abest velocity, and the trial velocities include: a trial velocitydetermined as a function of the best velocity and a trial velocityindependent of the best velocity.
 26. The method of claim 24, whereinthe slope of the at least one ridge is indicative of a best velocity,and the quality metric is determined using:$Q = \frac{P_{{BEST}\quad{VELOCITY}} - P_{REFERNCE}}{P_{{BEST}\quad{VELOCITY}} + P_{REFERNCE}}$where P_(best velocity) is the accumulated energy for k-ω pairs alongthe at least one ridge in a linear scale, P_(reference) is theaccumulated energy for k-ω pairs along the at least one ray in a linearscale, and Q is the quality metric.
 27. The method of claim 17, whereinthe slope of the at least one ridge is indicative of a best velocity,and the quality metric is determined using:$Q = \frac{P_{{BEST}\quad{VELOCITY}} - P_{REFERNCE}}{P_{{BEST}\quad{VELOCITY}} + P_{REFERNCE}}$where P_(best velocity) is the accumulated energy for k-ω pairs alongthe at least one ridge in a linear scale, P_(reference) is theaccumulated energy for k-ω pairs along the at least one ray in a linearscale, and Q is the quality metric.
 28. The method of claim 17, whereinthe parameter of the fluid includes at least one of: velocity of thefluid and speed of sound of the fluid.
 29. The method of claim 17,wherein the at least one ridge includes a first acoustic ridge in a leftplane of the k-ω plot and a second acoustic ridge in the right plane ofthe k-ω plot, and the method further comprises: summing the powersassociated with the k-ω pairs along the first and second acoustic ridgesto determine the accumulated energy for the at least one ridge.
 30. Themethod of claim 17, further comprising: comparing the quality metric toa threshold value, and determining the parameter of the fluid using theslope of the at least one ridge in response to the quality metricreaching the threshold value.
 31. A storage medium encoded withmachine-readable computer program code for measuring a parameter of afluid passing through a pipe using a spatial array of at least twosensors disposed at different axial locations along the pipe, each ofthe pressure sensors providing a time-domain signal indicative ofunsteady pressure within the pipe at a corresponding axial location ofthe pipe, the storage medium including instructions for causing acomputer to implement a method comprising: constructing from the signalsat least a portion of a k-ω plot, where the k-ω plot is indicative of adispersion relation for the unsteady pressure within the pipe, detectingat least one ridge in the k-ω plot, a slope of the at least one ridgebeing indicative of the parameter of the fluid, comparing an accumulatedenergy for k-ω pairs along the at least one ridge with an accumulatedenergy for k-ω pairs along at least one ray extending in the k-ω plot todetermine a quality metric indicative of a quality of the at least oneridge.
 32. The storage medium of claim 31, wherein the at least one rayhas a slope indicative of a reference velocity, and the method furthercomprises: determining accumulated energies for a plurality of rays inthe k-ω plot, the slopes of the plurality of rays indicating a pluralityof trial velocities, and selecting the reference velocity from the trialvelocities by comparing the accumulated energies for the plurality ofrays.
 33. The storage medium of claim 32, wherein the slope of the atleast one ridge is indicative of a best velocity, and the quality metricis determined using:$Q = \frac{P_{{BEST}\quad{VELOCITY}} - P_{REFRENCE}}{P_{{BEST}\quad{VELOCITYP}} + P_{REFRENCE}}$where P_(best velocity) is the accumulated energy for k-ω pairs alongthe at least one ridge in a linear scale, P_(reference) is theaccumulated energy for k-ω pairs along the at least one ray in a linearscale, and Q is the quality metric.